Can you find out the remainder when 3^300 is divided by 5?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

How many triangles are there in the picture below?

Can you make numbers like 24, using numbers 3,3,7 & 7 with any arithmetic operator?